DISCUSSION OF TAKE-HOME ASSIGNMENT #1 (Autumn 2009)
The overall results were quite good, with a mean score of 25.3 (84% of the 30 points possible), and a range from 16 to 30 (n=2). This indicates that most of you understood the material quite well. Please contact me if you want advice on how to do better on the second take-home assignment.
I have done my best to score the answers fairly. If you feel that you have not been given adequate credit for your answers, please submit a written challenge, along with your original answer, and I will review these carefully and respond.
1. Yasadat birth spacing [10 points possible]:
Lack's model of reproductive effort or "clutch size" assumes that available parental investment (PI) is finite, and that therefore any increase in fertility rate means each offspring receives less PI, which lowers offspring survival rates. The model also assumes that natural selection has "designed" parents to adjust their fertility and PI so as to maximize reproductive success = the number of surviving offspring (not necessarily through conscious choice, but through various physiological and cognitive mechanisms, some of which were mentioned in lecture notes and in Low's article). Finally, what makes it an ecological model is that it predicts that fertility is adjusted to ecological conditions so as to produce the locally optimal fertility rate or inter-birth interval (IBI). [By the way, "Yasadat" (and the data) are imaginary.]
a) For Yasadat birth spacing, Lack's model would predict that shorter IBIs (= higher fertility rates) lead to a smaller proportion of children surviving. The data in the table fit this prediction; for example, as we go from an IBI of 6 yrs to IBI=5, a smaller proportion of the children survive (0.9 vs. 0.8), and so on. But these are proportions surviving, and Lack's model recognizes that natural selection favors the IBI (or clutch/litter size) that maximizes the absolute number of surviving offspring (i.e., "reproductive success"). Therefore, your graph should display these numbers (obtained by multiplying number born times proportion surviving). (Click here to view such a graph.) Note that since the data you were given didn't include any information about the frequency of different IBIs among the Yasadat (only averages for each IBI), you couldn't actually test whether Yasadat women behave as predicted by Lack's model.
b) The optimal
IBI, as just noted, is the one that yields the largest number of
surviving offspring (maximum reproductive success) per parent; in
the Yasadat case, that is 4 yrs, since at this IBI 3.5 children
survive on average (5 born x 70% surviving). At shorter IBIs,
even though more children are born, higher mortality leads to
lower numbers of survivors; at longer IBIs, even though a higher proportion
survive, fewer total survive because of the low number born.
The assignment asked you to explain your answer in theoretical
terms, which many of you failed to do. The theoretical foundation of Lack's model is that natural selection
doesn't favor reproductive strategies that maximize fertility nor
those that minimize offspring mortality; rather, it favors those
that yield maximum number of surviving offspring, which sometimes
comes at the expense of less than maximal PI per offspring, and
hence less than maximum survivorship chances. A different
theoretical orientation -- for example, that of public
health -- might specify the optimal IBI as the one that minimized
child mortality (which in this data set, and many real-world
ones, would be a far lower fertility rate than the one that
maximizes reproductive success).
2. Optimal prey choice and the !Kung [20 points possible, 4 per section]:
To answer these questions correctly, you had to understand the optimal prey choice model (hereafter abreviated PCM), and explain how to apply its logic correctly to the situation. You also had to make some educated guesses about how to translate ethnographic statements about the !Kung (from Lee 1979) into the language of the PCM. I gave one point for each correct answer of "consistent" or "inconsistent," the other points being reserved for correct justification of conclusions. (By the way, Lee has repeatedly criticized optimal foraging models as being "too mechanical" to apply to humans, seemingly oblivious to the apparent fit of his ethnographic observations to the predictions of these models.)
a) Consistent. The PCM predicts that if "high-ranked" resources (those offering a higher return per unit handling time, a.k.a. "post-encounter return rate") are encountered at a high enough rate, "lower-ranked" (lower-return) resources will fall outside of the optimal array of prey types and will be ignored. Why? Because time spent handling (pursuing, capturing, processing) lower-ranked prey is time that can’t be spent searching for other prey (including any higher-ranked ones). When high-ranked resources become rare (or at least rarely encountered), the PCM predicts a "broadening" of the diet (i.e., expanded array of prey types pursued), adding prey types in decreasing rank order until the post-encounter rate of the next prey type is actually lower than the overall return rate from searching & handling the higher-ranked prey types. That's the scenario specified in this statement (assuming "desirable" = high-ranked, as seems reasonable): eat high on the hog when good stuff is plentiful, accept less desirable (lower-ranked) stuff when it's not. As I stressed in lecture, rank = value/handling time, but value is any currency that applies to all prey types (not necessarily calories); so "desirability" or "attractiveness" is a ranking criterion consistent with the PCM, as long as all prey types under consideration can all be ranked along this same scale.
b) Consistent. According to the PCM, prey types that are included in the optimal diet will be pursued whenever encountered; hence their frequency in the diet should be directly proportional to their encounter rate. Thus, a rare but highly-ranked prey type may be rarely encountered and thus rarely harvested (Kelly, p. 88), while another type that is abundant but low-ranked may be excluded from the optimal diet and thus always avoided despite its abundance. (A few people interpreted Lee to be saying that some species are never harvested because they are rare, but that's a misreading of his statement, which is that these are "rarely eaten," not that they are never eaten.)
c) Consistent. If "attractive" and "unrewarding" are taken as synonyms for "high-ranked" and "low-ranked", respectively, then this matches the PCM predictions; such an interpretation is plausible given that Lee states that the "attractive" prey are "large" while the "unrewarding" prey are small, and as noted in the Kelly reading, animal prey size usually correlates with returns (in weight, calories or protein) per unit handling time. "Plenty of meat from attractive large species" thus could translate as "high encounter rates with high-ranked prey types," leading to a relatively narrow optimal diet breadth that excludes many low-ranked prey types. On the other hand, the PCM predicts that !Kung outside the Dobe area who consume small, low-return prey types do so because larger (higher-ranked) types are less abundant; though Lee doesn't directly state this, it's implied in his remark that the Dobe !Kung "...have no need to bother with such unrewarding small creatures."
d) Inconsistent. The zebra is (1) "large" (suggesting high food value) and (2) "not...difficult to kill" (suggesting low handling costs, though this does not take processing costs into account); the most likely inference is thus that zebra would be high-ranked (i.e., would have a high post-encounter return rate). In any case, according to the PCM, the abundance or scarcity of a prey type should not affect its inclusion in the optimal diet. This is due to the simultaneous search assumption, which assumes that prey types are not searched for individually, but rather encountered in an opportunistic fashion, roughly in proportion to their abundance. It follows that zebra will be hunted whenever encountered (if in the optimal diet) or ignored (if not), regardless of their scarcity. Hence, Lee's explanation for why the !Kung never hunt zebra contradicts the PCM. Either he is wrong about why zebras are never hunted, or the !Kung don't follow the PCM in this case. (Some of you suggested that !Kung failure to hunt zebra must be due to a cultural taboo. While this is a plausible hypothesis, Lee never mentions such a taboo in his voluminous writings on the !Kung. An alternative, OFT-based hypothesis is that zebras occur in distant patches that have few other resources; I don't know if this hypothesis has any validity, but in any case lies outside the framework of the PCM.)
e) Consistent.
Recall the basic logic of the PCM: low encounter rates with
high-ranked prey leads to wider diet breadths in order to reduce
overall search costs. We normally think of encounter rates as
being determined by the environmental abundance of the prey type;
but since the PCM concerns the decisions of individual foragers,
what matters is not the absolute abundance of prey but the rate
at which individual foragers encounter them. If we hold prey
abundance constant and increase the number of foragers, we have
reduced encounter rate per forager just as effectively as if we
held foragers constant and reduced prey numbers (as stated in the lecture notes). Since the Tonga
are 100 times more numerous than the !Kung (because during normal
years they get most of their food from agriculture), if they
forage in an environment similar to that of the !Kung, we can
expect individual Tonga to encounter wild resources at
approximately 1/100th the frequency that the !Kung do.
Hence, the PCM would predict a much broader diet breadth,
consistent with the statement that they harvest 21 species known
to the !Kung but ignored by them (supporting the notion that
the environments are similar, and that the !Kung's narrower diet
breadth is a matter of choice). What the PCM adds here
is the insight that this difference occurs because the prey types
in question have low return rates, and hence will be ignored if
encounter rates with higher-ranked prey types are sufficiently
high. Note that there is no need for the Tonga to actually overharvest
prey in order to experience lower encounter rates -- their high
population density is sufficient to cause this (though any
overharvesting would intensify the trend).
References
Kelly, Robert L. (1995) The foraging spectrum: diversity in hunter-gatherer lifeways. Washington, D.C.: Smithsonian Institution Press.
Lack, David (1954) The evolution of reproductive rates. In Evolution as a Process, ed. J.S. Huxley, A.C. Hardy, and E.B. Ford, pp. 143-56. London: Allen and Unwin.
Lee, Richard B. (1979) The !Kung San: Men, Women and Work in a Foraging Society. Cambridge, New York: Cambridge University Press.